To study cancer, very powerful modern experimental methods -- including high-throughput approaches -- and modern statistics/computer-science methods are now used. Mechanistic quantitative models of cancer time-development, from very early stages to clinical disease, have been somewhat less well explored. A highly interdisciplinary, unusually closely interacting team of cancer biologists, molecular biologists, mathematicians, physicists, and computer scientists has been assembled to work toward dynamic, mechanistic carcinogenesis models so parsimoniously parameterized they have predictive capability. The overriding goal is to make the models more realistic and credible by taking into account the influence of intercellular interactions during carcinogenesis. The time-course of effects involving a diverse, interacting cell population and/or of tumor progression, a comparatively late stage in the lengthy cancer latency period, will be emphasized. The phenomena of microscopic tumor dormancy, recently found to be almost ubiquitous in humans, and of emergence from dormancy due to switching on of blood supply recruitment, will be one main focus. The team will work under an iterative paradigm: experiments, mathematical/computational model, experiments, etc. Data will be gathered from various sources: in vitro experiments, including modern high throughput results, and in depth studies of particular proteins; experiments using genetically engineered mice; highly developed imaging approaches; and results in the literature on human cancer incidence or mortality. Several of the individual projects will involve ionizing radiation, a carcinogen whose action has been unusually well characterized at very small time and length scales, as well as over a whole human lifetime and for whole organisms, so that it is highly informative about cancer development in general. Mathematical methods will include the following: classic mathematical biology approaches with systems of ordinary or partial differential equations; modern discrete and hybrid discrete-continuous models based on treating many cells, each represented as an entity which can interact with other cells and with its microenvironment according to comparatively simple rules, with complicated whole-system behavior arising from those rules; probabilistic stochastic-process models, needed since most new stages of cancer evolution putatively originate with a single cell at risk for eradication or accidental extinction; and multi time-scale computational modeling, in which effects governed by comparatively very short time scales influence much longer time-scale cancer evolution and vice-versa.